The consistency and consensus analysis for group decision-making with incomplete linguistic interval-valued intuitionistic fuzzy preference relations

This paper mainly provides a group decision-making (GDM) method based on linguistic interval-valued intuitionistic fuzzy preference relations (LIVIFPRs), where consistency and consensus analysis is conducted. The multiplicative consistency of LIVIFPRs is first introduced, and a consistency-based model is built to ascertain the missing values of an incomplete LIVIFPR. Considering the smallest distance, an optimization model is established to repair the unacceptably multiplicatively consistent LIVIFPR to have acceptable consistency. Meanwhile, the linguistic interval-valued intuitionistic fuzzy priority weights of LIVIFPR are constructed via the optimal solutions of a programming model. Then, Algorithm I for decision-making with one incomplete LIVIFPR is presented. For the GDM problem, the weights of experts are determined before aggregating the individual LIVIFPRs. Moreover, when the consensus of an individual LIVIFPR is unacceptable, a mathematical model is utilized to reach the consensus requirement. Subsequently, Algorithm II for GDM with incomplete LIVIFPRs is proposed step-by-step. Finally, the new GDM method is used to evaluate four Chinese express companies, and the advantages of this approach are demonstrated by performing a comparison analysis.